In a rocket, fuel burns at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to

Question

In a rocket, fuel burns at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to (A) 6000 N (B) 60000 N (C) 60 N (D) 600 N

Tardigrade Admin · Accepted Answer

Rate of burning of fuel ((d m/d t))=1 kg / s and velocity of ejected fuel (v)=60 km / s =60 × 103 m / s. Force = Rate of change of momentum =(d p/d t)=(d(m v)/d t)=v (d m/d t) =(60 × 103) × 1=60060 N .

Q. In a rocket, fuel burns at the rate of $1 k g / s$ . This fuel is ejected from the rocket with a velocity of $60 km / s$ . This exerts a force on the rocket equal to

6000 N

60000 N

60 N

600 N

Rate of burning of fuel $(\frac{d m}{d t}) = 1 k g / s$
and velocity of ejected fuel $(v) = 60 km / s$
$= 60 \times 1 0^{3} m / s$ .
Force $=$ Rate of change of momentum
$= \frac{d p}{d t} = \frac{d ( m v )}{d t} = v \frac{d m}{d t}$
$= (60 \times 1 0^{3}) \times 1 = 60060 N .$

Q. In a rocket, fuel burns at the rate of 1kg/s. This fuel is ejected from the rocket with a velocity of 60km/s. This exerts a force on the rocket equal to